On the Lp-theory for second-order elliptic operators in divergence form with complex coefficients.

Autor: ter Elst, A. F. M., Haller-Dintelmann, R., Rehberg, J., Tolksdorf, P.
Zdroj: Journal of Evolution Equations; Dec2021, Vol. 21 Issue 4, p3963-4003, 41p
Abstrakt: Given a complex, elliptic coefficient function we investigate for which values of p the corresponding second-order divergence form operator, complemented with Dirichlet, Neumann or mixed boundary conditions, generates a strongly continuous semigroup on L p (Ω) . Additional properties like analyticity of the semigroup, H ∞ -calculus and maximal regularity are also discussed. Finally, we prove a perturbation result for real coefficients that gives the whole range of p's for small imaginary parts of the coefficients. Our results are based on the recent notion of p-ellipticity, reverse Hölder inequalities and Gaussian estimates for the real coefficients. [ABSTRACT FROM AUTHOR]
Databáze: Complementary Index
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